One triangle shown is formed by the tree, its shadow, and a line of sight from the ground to the top of the tree. The other is formed by Manny, his shadow, and a line of sight from the ground to the top of his head. Are the two triangles similar?

Answer:

1. 8t

2. 510 + 6t

3. 510 - 2t

Step-by-step explanation:

1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t

2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t

3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.

d' = 510 + 6t - 8t

= 510 - 2t  

The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

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Answer:

A) (1)/(7)

B) 33

Step-by-step explanation:

For (A), the sequence follows in 1 divided by numbers in a consecutive order, therefore after (1)/(6), the next term is (1)/(7)

For(B), the sequence follows in multiples of three but skips one in between

Example: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36...

In the sequence, 6, 12, 18 and 24 are skipped, meaning that the next number to be skipped is 30, hence 33 is the next number in the sequence.

Because all the numbers in the sequence are odd numbers we can say that the sequence follows in odd consecutive numbers which are multiples of 3.

To find the distance between the man's starting point and his final position, we can use vector addition.

Let's call the man's starting point A and his final position B. We can represent the two legs of his journey as vectors A and B, respectively.

The first leg of his journey, due west, can be represented as a vector of magnitude 4 km in the -x direction.

The second leg of his journey, on a bearing of 197°, can be represented as a vector in the -x and -y direction. We can use trigonometry to find the components of this vector.

The x component of the vector can be found using the formula:

x = magnitude * cos(angle) = d * cos(197°)

The y component of the vector can be found using the formula:

y = magnitude * sin(angle) = d * sin(197°)

where d is the magnitude of the vector (the distance the man traveled in this leg of his journey).

To find the magnitude of the vector, we'll use the Pythagorean theorem:

d^2 = x^2 + y^2

We can substitute the x and y components we found above into this equation to find d:

d^2 = (d * cos(197°))^2 + (d * sin(197°))^2

d^2 = d^2 * (cos^2(197°) + sin^2(197°))

d^2 = d^2

d = sqrt(d^2) = sqrt(d^2)

So the magnitude of the vector is d.

Next, we can add the two vectors to find the total distance from the man's starting point to his final position:

distance = sqrt((4 - d * cos(197°))^2 + (d * sin(197°))^2)

This is the distance the man is from his starting point. To find the exact value, we would need to know the value of d. However, without that information, this is as far as we can take the calculation.

The expression that illustrate the diagram below is f(x) = 47-2x

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

In the diagram, the total no of box is 45 and 2 boxes are missing on the second box. Therefore the constant in the the expression is 45+2 = 47. Let x be the variable.

Therefore f(x) = 47-2x

when it is pattern 1

x= 1

f(1) = 47-2 = 45

when it's pattern 2

f(x) = 47-2×2 = 43

when it's pattern 3

f(x) = 47- 2×3 = 41

therefore the expression that can illustrate the diagrams is f(x) = 47-2x

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The solution to the system of equations is x = -3 and y = -4.

To solve the system of equations:

Equation 1: 2x - y = -10

Equation 2: 3x + 2y = -1

We can use the method of substitution or elimination to find the values of x and y.

Let's use the method of elimination:

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(2x - y) = 2(-10)

4x - 2y = -20

Now, we can eliminate y by adding Equation 2 and the modified Equation 1:

(3x + 2y) + (4x - 2y) = -1 + (-20)

7x = -21

x = -3

Substitute the value of x into Equation 1 to solve for y:

2(-3) - y = -10

-6 - y = -10

y = -10 + 6

y = -4

Therefore, the solution to the system of equations is x = -3 and y = -4.

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Answer:

The answer is 32

Step-by-step explanation:

The formula for finding the area of a trapezoid is:

         ((base 1 + base 2)/ 2 )* h

Now all you have to do is substitute the numbers in.

Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.

Answer:

32 square units

Step-by-step explanation:

\(\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32\)

Note that \(b_1\) and \(b_2\) are the lengths of each base of the trapezoid, so it doesn't matter which is which.

Answer:

Jesus are you 2 years old the answer is 3.

Step by step:

There is one more girl for every 5 boys, and there is 33 students in total, there is 11 in total for each, and 11 times 3 = 33.

Answer:

39 3/8 ft ^2

Step-by-step explanation:

To find the area of a rectangle, multiply the length times the width.

A = l*w

  = 7 1/2  * 5 1/4

Change the mixed numbers to improper fractions.

A = 15/2 * 21/4

    =315/8

Change back to a mixed number.

8 goes into 315 39 times with 3 left over.

 = 39 3/8

Answer:

(you can round to 39.4)

Step-by-step explanation:

Find the area of the rectangle shown

7 1/2 ft

5 1/4ft

7 1/2 = 7.5 ft

5 1/4 = 5.25 ft

Area = L x W

Area = 7.5 x 5.25

Area = 39.375

Answer:

an outlier is a number that is at least 2 standard deviations away from the mean for example in the set 1,1,1,1,1,1,1,1,1,7,7,7 would be the outlier

Step-by-step explanation:

watashi wa sore ga tadashī koto o negatte imasu

arigatozaimasu!!

Step-by-step explanation:

i have noooo idea but ayyeee

We are asked to use the formula for the area of a triangle based on an image.

Please provide the image.

The area of the triangle is: base x height / 2

The base is 13 m and the height is 8 m

then we have:

Area = 13 m x 8 m / 2 = 52 m^2 (fifty two square meters)

The metric conversion from 195 km/h to m/min is; 3250 m/min

The basic metric conversion units are meters (for length), grams (for mass or weight), and liters (for volume).

Now, the metric unit of conversion from km/h to m/min is;

1 km/h = 50/3 m/min

Thus;

195 km/h = (195 * 50)/3

= 3250 m/min

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Answer:

48%

Step-by-step explanation:

I like to look at percentages as test grades. If you got a 130/250 on a test, you would simply need to view the dash line as a 'divided by'. So you would figure 130 divided by 250 is .52, or 52%... Then, you would need to subtract 52 from 100 to get 48% to get the percentage of people who do not walk to school.

48%

48% of 250 is 120

120+130=250

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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Answer:

\(1\frac{92}{99}\)

Step-by-step explanation:

\(\frac{191}{99} = \frac{99 + 92}{99}\)

     = \(1\frac{92}{99}\)

Sorry, don't know if that answers your question.

Step-by-step explanation:

hope you can understand

The theoretical probability of spinning red is given as follows:

1/3.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the spinner in this problem, 2 out of 6 regions are red, hence the theoretical probability is given as follows:

2/6 = 1/3.

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Answer:

Step-by-step explanation:

A = l*w

13.5 * 10.67 = 144.045 or 144

Hope that helps!

Answer:

Step-by-step explanation:

Plug in the values of x in the equation and find the value of y

6) y = - 3x + 5

Plugin x = -1 , y = -3*(-1) + 5 = 3 + 5 = 8     (-1 , 8)

Plugin x = 1 ;  y = -3*1 + 5    = - 3 + 5 = 2   (1, 2)

Plugin x = 3 ; y = -3*3 + 5 = -9 + 5   = -4   (3,  -4)

Plugin x = 4 ; y  = -3*4 + 5 = -12+5  = -7   (4 , - 7)

7) y = -4x

Plugin x = -2 ; y = -4*(-2) = 8          (-2 , 8)

Plugin x = -1 ; y = -4 *(-1) = 4          (-1 , 4)

Plugin x = 0 ; y = 0                       (0 , 0 )

Plugin x = 2; y = -4*2 = -8            (2 , -8)

The equation of the line is with the coordinates f(-6) = 9 and f (20) = 5. is y = (-2/13)x + 117/13.

Y = mx + b, where m is the line's slope and b is the y-intercept, is the slope-intercept form of a linear equation. This form is helpful since it provides information about the line's slope and y-intercept in a clear and understandable manner. We can quickly determine the slope of the line (m) and its point of intersection with the y-axis by glancing at the equation (b). By beginning at the y-intercept and using the slope to determine other locations along the line, we can also graph the line using this method.

The slope of the line is given as:

m = (y2 - y1) / (x2 - x1)

Substitute the given coordinates:

m = (5 - 9) / (20 - (-6))

m = -4 / 26

m = -2 / 13

Using the point slope form we have:

y - y1 = m(x - x1)

Using the point (-6, 9):

y - 9 = (-2/13)(x - (-6))

y - 9 = (-2/13)x - 12/13

y = (-2/13)x + 117/13

So the equation of the line is y = (-2/13)x + 117/13.

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A regression through the origin is a linear regression model where the intercept time period is assumed to be 0, meaning the regression line passes through the starting place.

This version is also referred to as zero-intercept regression or homogeneous regression.

It's far frequently used whilst there's a theoretical foundation to agree with that the relationship among the dependent and unbiased variable passes via the foundation or whilst the information propose that the intercept ought to be 0.

The slope coefficient represents the change within the structured variable for a one-unit increase inside the unbiased variable.

However, this kind of regression may not be appropriate in all cases, and a general linear regression version with an intercept term can be greater suitable.

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Answer:

-2<=y<=-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

ANSWER:

D. g(x) = -lxl

STEP-BY-STEP EXPLANATION:

Each absolute value graph will have a “V” shape. It consists of two parts: one with a negative slope and one with a positive slope. The point of intersection is called the vertex. An absolute value graph is symmetric, meaning that it can be folded in half along its line of symmetry.

In this case, it is an intervened V, which means that it has a minus sign that makes it reflect on the x-axis.

Therefore, the correct answer is: D. g(x) = -lxl

Answer:

175

Step-by-step explanation:

You have to divide 15,050 by 86

Have a nice day !

Answer:

≥ 34.29 mph

Step-by-step explanation:

Given that:

Distribution is normal :

Mean(m) = 31 mph

Standard deviation = 2 mph

Speed of top 5%

Top 5% = bottom (100% - 5%) = 95% = 0.95

Zscore which corresponds to 0.95 = 1.645

Using the Z formula:

Zscore = (score - mean) / standard deviation

1.645 = ( score - 31) / 2

Croas multiply:

2 * 1.645 = score - 31

3.29 = score - 31

3.29 + 31 = score

34.29 = score

Hence, speed must be greater than or equal to 34.29 mph

The equation of the normal line to the curve x^2y^2 = 4 at the point (-1,-2) is y = x - 1.

To find the tangent line and normal line to the curve x^2y^2 = 4 at the point (-1,-2), we need to determine the derivative of the curve equation with respect to x and evaluate it at the given point.

First, let's differentiate the equation x^2y^2 = 4 implicitly with respect to x using the chain rule:

2x * (y^2) + 2y * (2xy * dy/dx) = 0

Simplifying the equation, we have:

2xy^2 + 4xy(dy/dx) = 0

Now, let's find the value of dy/dx at the point (-1,-2). Substitute x = -1 and y = -2 into the equation:

2*(-1)(-2)^2 + 4(-1)*(-2)(dy/dx) = 0

Simplifying further:

8 + 8(dy/dx) = 0

8(dy/dx) = -8

dy/dx = -1

We have found the derivative dy/dx at the point (-1,-2), which is -1. This represents the slope of the tangent line to the curve at that point.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - y₁ = m(x - x₁)

Substituting the values of (-1,-2) and dy/dx = -1 into the equation, we have:

y - (-2) = -1(x - (-1))

y + 2 = -1(x + 1)

y + 2 = -x - 1

y = -x - 3

Therefore, the equation of the tangent line to the curve x^2y^2 = 4 at the point (-1,-2) is y = -x - 3.

To find the normal line, we know that the slope of the normal line is the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is 1.

Using the point-slope form of a line again, we can write the equation of the normal line as:

y - y₁ = m'(x - x₁)

Substituting the values of (-1,-2) and m' = 1 into the equation, we have:

y - (-2) = 1(x - (-1))

y + 2 = x + 1

y = x - 1

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\(\begin{array}{r|l}576&2\\288&2\\144&2\\72&2\\36&2\\18&2\\9&3\\3&3\\1\end{array}\)

\(576=2^6\cdot3^2\)

Therefore

\(4\sqrt{576}=4\sqrt{2^6\cdot3^2}\)

All the ordered pairs that represent points on the graph of this equation include the following:

A. (-4, 4).

C. (-2, 1)

E. (2, -5)

F. (0, -2)

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of the given function, we would plot its equation by using an online graphing calculator and then read all the ordered pairs that lie on the line.

By critically observing the graph of the given function (see attachment), the solutions are include following;

Ordered pair = (-4, 4).

Ordered pair = (-2, 1).

Ordered pair = (2, -5).

Ordered pair = (0, -2).

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Complete Question:

Which ordered pairs represent points on the graph of this equation? Select all that apply.

2y= –3x–4

(-4, 4)

(7, 6)

(-2, 1)

(0, 7)

(2, -5)

(0, -2)

\(xy - 2x = - 3\)

\(xy = 2x - 3\)

____________________________________________

\(3 {x}^{2} + 5xy + 4 = 0\)

\(3 {x}^{2} + 5(2x - 3) + 4 = 0\)

\(3 {x}^{2} + 10x - 15 + 4 = 0\)

\(3 {x}^{2} + 10x - 11 = 0\)

\(delta = {10}^{2} - 4(3)( - 11)\)

\(delta = 100 + 132\)

\(delta = 232\)

Thus;

\(x = \frac{ - 10 + \sqrt{232} }{6} \: \: or \: \: x \frac{ - 10 - \sqrt{232} }{6} \\ \)

\(x = \frac{ - 10 + 15.23}{6} \: \: or \: \: x = \frac{ - 10 - 15.23}{6} \\ \)

\(x = \frac{5.23}{6} \: \: or \: \: x = \frac{ - 25.23}{6} \\ \)

\(x = 0.8716 \: \: or \: \: x = - 4.205\)

____________________________________________

\(0.8716 \: y = 2(0.8716) - 3\)

\(0.8716 \: y = 1.7432 - 3\)

\(0.8716 y= - 1.2568\)

\(y = \frac{ - 1.2568}{0.8716} \\ \)

\(y = - 1.4419\)

\( - 4.205 \: y = 2( - 4.205) - 3\)

\( - 4.205 \: y = - 8.410 - 3\)

\( - 4.205 \: y = - 11.410\)

\(y = \frac{ - 11.410}{ - 4.205} \\ \)

\(y = 2.7134\)

And we're done

Have a great day ♡